Clearly, FPT \(\subseteq \)  XP, and so the study of parameterized complexity often focuses on determining whether or not a problem is in FPT.
Like P \(\ne \)  NP, FPT \(\ne \)  W[1] is the basic complexity assumption at the foundation of parameterized algorithms.
W[1]-hardness is proven using parameterized reductions which are similar to standard NP-hardness reductions but with additional requirements on the translation of the parameter.
In this paper, we prove W[2]-hardness (an even stronger notion [1]}) via parameterized reductions from Set Cover.
